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shuangzili · 2022年03月23日

不明白

NO.PZ2016021705000030

问题如下:

Happy Resorts Company currently has 1.2 million common shares of stock outstanding and the stock has a beta of 2.2. It also has $10 million face value of bonds that have five years remaining to maturity and 8 percent coupon with semi-annual payments, and are priced to yield 13.65 percent. If Happy issues up to $2.5 million of new bonds, the bonds will be priced at par and have a yield of 13.65 percent; if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16 percent. Happy has learned that it can issue new common stock at $10 a share. The current risk-free rate of interest is 3 percent and the expected market return is 10 percent. Happy's marginal tax rate is 30 percent. If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio, its weighted average cost of capital is closest to:

选项:

A.

14.5 percent.

B.

15.5 percent.

C.

16.5 percent.

解释:

B is correct.

Capital structure:Market value of debt: FV = $10,000,000, PMT = $400,000, N = 10,I/YR = 13.65%/2. Solving for PV gives the answer $7,999,688.Market value of equity: 1.2 million shares outstanding at $10 = $12,000,000

To raise $7.5 million of new capital while maintaining the same capital structure, the company would issue $7.5 million × 40% = $3.0 million in bonds, which results in a before-tax rate of 16 percent.

rd(1 t) = 0.16(1 0.3) = 0.112 or 11.2%

re = 0.03 + 2.2 (0.10 0.03) = 0.184 or 18.4%

WACC = [0.40(0.112)] + [0.6(0.184)] = 0.0448 + 0.1104 = 0.1552 or 15.52%

Happy Resorts Company currently has 1.2 million common shares of stock outstanding and the stock has a beta of 2.2. It also has $10 million face value of bonds that have five years remaining to maturity and 8 percent coupon with semi-annual payments, and are priced to yield 13.65 percent. If Happy issues up to $2.5 million of new bonds, the bonds will be priced at par and have a yield of 13.65 percent; if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16 percent. Happy has learned that it can issue new common stock at $10 a share. The current risk-free rate of interest is 3 percent and the expected market return is 10 percent. Happy's marginal tax rate is 30 percent. If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio, its weighted average cost of capital is closest to:

您的回答A, 正确答案是: B

A

不正确14.5 percent.

B

15.5 percent.

C

16.5 percent.


To raise $7.5 million of new capital while maintaining the same capital structure, the company would issue $7.5 million × 40% = $3.0 million in bonds, which results in a before-tax rate of 16 percent.

rd(1 − t) = 0.16(1 − 0.3) = 0.112 or 11.2%

re = 0.03 + 2.2 (0.10 − 0.03) = 0.184 or 18.4%

WACC = [0.40(0.112)] + [0.6(0.184)] = 0.0448 + 0.1104 = 0.1552 or 15.52%


问题1

7,999,688我算出来了,1.2millions of common shares of stock是指市值还是股票数量,我看老师回答里面有人问,老师回答是股票数量,但这里奇怪,Happy has learned that it can issue new common stock at $10 a share,这里应该用的是债券和股票的market value对吗?,发行价10元是primary market,二级市场可高可低,一级市场的股票价格算market value of stock price吗?


问题2:我没看懂后面40% 60%,股债比应该是7999688/12000000把?这个结果是0.66,和40% 60%没关系?这数字哪里来的?


问题3:If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio。那就是股债比和之前一样是0.66? new capital指的是股票+债券对吗?因为这里没有明确说raise 啥


问题4:16%不是entire issuance吗?应该是债加股才对?这里答案怎么用到债券上了?


谢谢,请讲下求出7999688以后的解题思路



1 个答案

王琛_品职助教 · 2022年03月24日

嗨,努力学习的PZer你好:


1)7,999,688我算出来了,1.2millions of common shares of stock是指市值还是股票数量,我看老师回答里面有人问,老师回答是股票数量,但这里奇怪,Happy has learned that it can issue new common stock at $10 a share,这里应该用的是债券和股票的market value对吗?,发行价10元是primary market,二级市场可高可低,一级市场的股票价格算market value of stock price吗?

根据题干的已知条件,这个信息,是用于计算在外发行的股票的市值的

因为前面提到了在外发行的股票数量是 1.2 m,又通过这句话提到股价是 10 元,所以得到股票的市值是 12 m

当然这里同学可能会有疑问,就是为何新股的发行价,能用来计算股票的市值,请参考:https://class.pzacademy.com/qa/95700

2)我没看懂后面40% 60%,股债比应该是7999688/12000000把?这个结果是0.66,和40% 60%没关系?这数字哪里来的?

同学算的股债比没错,是 D/E 

但是我们计算 WACC 时,用的是 wd 和 we,即 D/(D+E) 和 E/(D+E)

对应到题目,相当于 wd = 800 万 / (800 万 + 1200 万) = 40%

we = 1200 万 / (800 万 + 1200 万) = 60%

3)If Happy raises $7.5 million of new capital while maintaining the same debt-to-equity ratio。那就是股债比和之前一样是0.66? new capital指的是股票+债券对吗?因为这里没有明确说raise 啥

是的,保持同样的股债比,所以 wd = 40%,we = 60%

new capital 是指股票和债券

4)16%不是entire issuance吗?应该是债加股才对?这里答案怎么用到债券上了?

16% 并不是股票加债券的融资成本,仅是指债券的融资成本

if it issues bonds beyond $2.5 million, the expected yield on the entire issuance will be 16 percent.

是说,如果债券的融资规模大于 2.5 m,那么融资成本就套用 16%

之所以说 entire issuance,是因为可能会有同学将融资规模按阶梯计算

就拿这道题的债券融资规模为 3 m 举例,按阶梯计算成本是说,2.5 m 用 13.65% 算,然后超过 2.5 m 的部分,即 0.5 m,按 16% 算

题干是想简化计算,别弄那么复杂,所以说 entire issuance,即只要融资规模大于 2.5 m,不管是多少,都统一按 16% 计算,不需要按阶梯计算融资成本

5)谢谢,请讲下求出7999688以后的解题思路

根据上面的回答,我理解已经把后面的解题思路说清楚了哈

同学如果还是有疑问,可以就具体问题,通过追问或者评论形式提出,我会再继续回答

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